A regular polygon of n sides is formed by bending a wire of total length `2 pi r` which carries a current i. (a) Find the magnetic field B at the centre of the polygon. (b) By letting `n rarr oo` , deduce the expression for the magnetic field at the centre of a circular current.

Options

A. `B=(mu_0I)/(2sqrt2pi)`
B. `B=(mu_0I)/(2sqrt3pi)`
C. B is parallel to the z-axis
D. B makes an angle of `45^@` with the x-y plane

Answer

(a,d)

Explanation

The magnitude of the magnetic field depends only on the distance
from the x-axis. Point A and C are at distance of 1 unit each
from the x-axis. Points B and D are at distance of `sqrt2` unit each
from the x-axis. Magnetic field at point D,
`B=(mu_0I)/(1sqrt2pi)`
It is obvious that B is inclined at an angle of `45^@` with the
x-y plane.